It is possible, but it's a labour-intensive and pricey proposition. Your controls won't fit on a drop bar (they're a different diameter) so you'd need new brake levers and shifters; brifters are very expensive, so separate brake levers and bar-end shifters would be the way to go. Also, since you have v-brakes, you would need to use a travel agent to work with the drop bar levers (it's the little pulley replacing the noodle at the top of the brake arm):



If you're after more hand positions you could use some bar ends (I like these) or some trekking bars like I have on one of my bikes: